20 1 1 Answers to liberal arts mathematics in Sichuan college entrance examination

20 1 1 National Unified Examination for Enrollment of Ordinary Colleges and Universities

An analysis of Sichuan literature and mathematics

1. answer: B.

Analysis: If M= {1, 2,3,4,5} and n = {2,4}, then N={ 1, 2,3}.

2. Answer: B

Analysis: There are 12+7+3=22 frequencies * * greater than or equal to 3 1.5, so P= =.

3. Answer: D

Analysis: If the center coordinate is (2, -3).

4. A: A.

Analysis: the inverse function can be known from the symmetry of the image of the function about the straight line y=x, so choose a.

5. A: A.

Analysis: "x=3" is the necessary and sufficient condition and the unnecessary condition of "x2=9".

6. Answer: B

Analysis: If, then, there are three positional relationships, which may be parallel, intersecting or different planes, so A is incorrect. Although ∨∨, or * * *, it may be a * * * plane, or it may not be a * * * plane, so C and D are also incorrect.

7. Answer: D

Parse: = = =.

8. Answer: C

Analysis: Judging from the meaning of the question,

, .

9. A: A.

Analysis: A2 = 3 = 3× 40, A3 = 12 = 3× 4 1, A4 = 48 from A 1, AN+ 1.

10. answer: C.

Analysis: according to the meaning of the question, if car A and car B are launched on the same day, they will get profits, draw constraints and substitute the points in the feasible region into the objective function.

1 1. answer: a.

Analysis: If the abscissa is 0 and the slope of the straight line passing through the coordinates of two points is 0, let the straight line equation be 0, then.

12. Answer: B.

Analysis: basic events:. The number of parallelograms with an area of 2; M=3。

13. Answer: 84

Analysis: The coefficient in the expansion is =84.

14. Answer: 16

Analysis: this point is obviously on the right branch of hyperbola, and the distance from this point to the left focus is 20, so

15. Answer:

When parsing:, then =.

16. Answer: 234

17. This topic mainly investigates independent events, mutually exclusive events's concepts and related calculations, and examines the ability to solve practical problems by using the knowledge and methods learned.

Analysis: ① There is =, but -2≠2, then ① is incorrect; The proposition equivalent to "If there is always time" is "If there is always time", so ② ③ is correct; If the function f(x) is monotonous in the definition domain, then it must be a single function, and then ④ is correct.

Analysis: (1) The probability that Party A and Party B will return the car within 3 hours or more and 4 hours or less respectively is, so the probability that Party A and Party B will return the car within 3 hours or more and 4 hours or less is.

(2) Let "Party A and Party B rent a car for no more than two hours at a time" as event A, "Party A and Party B rent a car for no more than two hours at a time, and the other party returns the car for no more than two hours and no more than three hours" as event B, and the sum of the car rental fees paid at this time is 2 yuan; "Party A and Party B return the car for more than two hours and not more than three hours at a time" is Event C, and the sum of the car rental fees paid at this time is 4 yuan; Event d is that one person rents a car for no more than two hours at a time, and the other person returns the car for no more than three hours and no more than four hours. The total rental fee paid at this time is 4 yuan; Then,,,.

Because events A, B, C and D are mutually exclusive, the sum of car rental fees paid by both parties is less than the probability of 6 yuan.

Therefore, the sum of the rental fees paid by both parties is less than the probability of 6 yuan.

18. This topic examines the properties of trigonometric functions, the relationship between trigonometric functions with the same angle, the sine and cosine formulas, the inductive formula of the sum of two angles and other basic knowledge and basic operational ability, functions and equations, transformation and transformation and other mathematical ideas.

Analysis: (I) √

(ii) by,

By,

Two formulas add up to two.

19. This topic mainly examines the basic knowledge such as nature, line-plane relationship, dihedral angle, spatial imagination and logical reasoning ability, as well as the ability to solve problems with vector knowledge.

Solution 1:

(I) connect AB 1 and BA 1 at point o, and connect OD,

∫c 1d∑aa 1，A 1C 1=C 1P，∴AD=PD.

Ao = b 10。 ∴od∑PD 1。

OD plane BDA 1, PD 1 plane BDA 1.

∴PB 1∥ aircraft BDA 1.

(ii) Make AE⊥DA 1 at point E, and then Be.

∵BA⊥CA, BA⊥AA 1 and AA 1∩AC=A, ba ⊥ plane aa1c1c.

According to the theorem of three perpendicular lines, it becomes ⊥ da 1. Bea is the plane angle of dihedral angle a-a1d-B.

At Rt△A 1C 1D, it is ∴.

In Rt△BAE, ∴.

So the plane angle cosine of dihedral angle A-A 1d-B is.

Solution 2:

As shown in the figure, taking A 1 as the origin, the straight lines of A 1B 1 C1A are the X-axis, Y-axis and Z-axis respectively to establish the spatial rectangular coordinate system A1.

(I) in PAA 1, there are C 1D= AA 1+0, ∫AC∑PC 1, ∴.

∴ , , .

Let the normal vector of the plane BA 1D be,

Then do it.

∫Pb 1∑ plane BA 1D,

∴ ,

∴PB 1∥ aircraft BDA 1.

(ii) According to (i), the normal vector of the plane BA 1D is known.

It is also the normal vector of plane aa1d.

So the plane angle cosine of dihedral angle A-A 1d-B is.

20. This paper examines the basic knowledge of geometric series and arithmetic progression, basic calculation ability, ability to analyze and solve problems, and mathematical ideas such as transformation and transformation.

Analysis: (1) From the known, =, ∴,,

When you become arithmetic progression, you can get it.

Simplify the complex and get a solution.

(ii) If = 1, then () every item =, at this time,, obviously becomes arithmetic progression.

If ≠ 1,,, becomes arithmetic progression, you can get +=2.

That is,+= drops to+=.

∴ + =

∴, become arithmetic progression.

2 1. This small question mainly examines the basic knowledge such as the standard equations and basic properties of straight lines and ellipses, and examines the thinking method and reasoning operation ability of plane analytic geometry.

(i) It is known that, therefore, the elliptic equation is.

The right focus of the ellipse is (,0), and the equation of the straight line is,

7 -8 =0, and substitute it into the elliptic equation. The solution is =0, =,

Substituting into the linear equation gives = 1. The coordinates of point =-.∴d are

Then the length of the line segment.

(2) When the straight line is perpendicular to the X axis, it is inconsistent with the meaning of the question.

Let the equation of a straight line be (and).

Substitution into elliptic equation is simplified as (4k2+ 1) -8k =0, and the solution is =0, =,

Let = 1。 The coordinates of point =.∴d are,

The equation of straight line AC is +y= 1, and the equation of straight line BD is:

Simultaneous solution, so the coordinates of Q point are also,

∴ .

So it is a fixed value.

22. This topic mainly examines the application of basic knowledge such as function derivation, inequality proof and equation solution, and examines mathematical thinking methods such as combination of numbers and shapes, function equation, classification and integration, special and general, and the ability of reasoning, operation, analysis and problem solving.

Solution: (i) f (x) =18f (x)-x2 [h (x)] 2 =-x3+12x+9 ()

∴ -3x2+ 12，make，get (x=-2 shed)。

When,; When.

Therefore, when it is an increasing function; When it is a decreasing function.

The maximum value of the function at.

(ii) The original equation can be changed into:

① If the original equation has a solution;

② If the original equation has two solutions;

③ If the original equation has a solution;

④ When or, the original equation has no solution.

(iii) by the known.

f(n)h(n)- = -